1. Field of the Invention
The present invention relates to generalizations of adjoint networks techniques and, more particularly, to generalizations of adjoint networks techniques for RLC interconnects model-order reductions.
2. Description of Related Art
With the advances in deep submicron semiconductor techniques, the parasitic effects of interconnects can no longer be ignored. To completely characterize the signal integrity issues, interconnects are often modeled as large RLC networks. To this end, in order to reduce the computational time of the large-scale RLC interconnect networks, model-order reduction methods have emerged recently.
A consensus has emerged that of the many model-order reduction techniques, the moment matching approach, or the so-called Krylov subspace projection method, seems to be the most viable one. In general, these methods can be divided into two categories: one-sided projection methods and two-sided projection methods. The one-sided projection methods use the congruence transformation to generate passive reduced-order models, while the two-sided ones can not be guaranteed. In recent works, the adjoint network reduction technique has been proposed to further reduce the cost about yielding the congruence transformation matrix. The method was suitable for analyzing the special multi-port driving-point impedance of RLC interconnect circuits.
The purpose of the present invention is to extend the adjoint network technique for general RLC interconnect networks. First, relationships between an original MNA network and its corresponding adjoint MNA network are explored. Second, the congruence transformation matrix can be constructed by using the resultant biorthogonal bases from the Lanczos-type algorithms. Therefore, less storage and computational complexity are required in the technique of the present invention.